Polar Codes with Higher-Order Memory

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dc.authoridAfser, Huseyin/0000-0002-6302-4558
dc.contributor.authorAfser, H.
dc.contributor.authorDelic, H.
dc.date.accessioned2025-01-06T19:11:30Z
dc.date.available2025-01-06T19:11:30Z
dc.date.issued2018
dc.description.abstractWe introduce a construction of a set of code sequences {C-n((m)) : n 1, m 1} with memory order m and code length N(n). {C-n((m))} is a generalization of polar codes presented by Arkan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n - 1) and N(n - m), and {C-n((m))} coincides with the original polar codes when m = 1. We show that {C-n((m))} achieves the symmetric capacity I(W) of an arbitrary binary-input, discrete-output memoryless channel W for any fixed m. We also obtain an upper bound on the probability of block-decoding error P-e of {C-n((m))} and show that Pe=O(2-N) is achievable for < 1/[1+m(phi - 1)], where phi (1, 2] is the largest real root of the polynomial F(m, ) = (m) - (m - 1) - 1. The encoding and decoding complexities of {C-n((m))} decrease with increasing m, which proves the existence of new polar coding schemes that have lower complexity than Arkan's construction.
dc.description.sponsorshipBogazici University Research Fund [11A02D10]; Aselsan Elektronik A.S.
dc.description.sponsorshipThis work was supported by Bogazici University Research Fund under Project 11A02D10. H. Afser was also supported by Aselsan Elektronik A.S.
dc.identifier.doi10.1134/S0032946018040014
dc.identifier.endpage328
dc.identifier.issn0032-9460
dc.identifier.issn1608-3253
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85060767898
dc.identifier.scopusqualityQ3
dc.identifier.startpage301
dc.identifier.urihttps://doi.org/10.1134/S0032946018040014
dc.identifier.urihttps://hdl.handle.net/20.500.14669/3382
dc.identifier.volume54
dc.identifier.wosWOS:000456991400001
dc.identifier.wosqualityQ4
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMaik Nauka/Interperiodica/Springer
dc.relation.ispartofProblems of Information Transmission
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_20241211
dc.titlePolar Codes with Higher-Order Memory
dc.typeArticle

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